• Frame covariant formalism for fermionic theories

      Finn, Kieran; orcid: 0000-0002-9840-2264; email: kieran.finn@manchester.ac.uk; Karamitsos, Sotirios; Pilaftsis, Apostolos (Springer Berlin Heidelberg, 2021-07-02)
      Abstract: We present a frame- and reparametrisation-invariant formalism for quantum field theories that include fermionic degrees of freedom. We achieve this using methods of field-space covariance and the Vilkovisky–DeWitt (VDW) effective action. We explicitly construct a field-space supermanifold on which the quantum fields act as coordinates. We show how to define field-space tensors on this supermanifold from the classical action that are covariant under field reparametrisations. We then employ these tensors to equip the field-space supermanifold with a metric, thus solving a long-standing problem concerning the proper definition of a metric for fermionic theories. With the metric thus defined, we use well-established field-space techniques to extend the VDW effective action and express any fermionic theory in a frame- and field-reparametrisation-invariant manner.
    • Frame covariant formalism for fermionic theories

      Finn, Kieran; orcid: 0000-0002-9840-2264; email: kieran.finn@manchester.ac.uk; Karamitsos, Sotirios; Pilaftsis, Apostolos (Springer Berlin Heidelberg, 2021-07-02)
      Abstract: We present a frame- and reparametrisation-invariant formalism for quantum field theories that include fermionic degrees of freedom. We achieve this using methods of field-space covariance and the Vilkovisky–DeWitt (VDW) effective action. We explicitly construct a field-space supermanifold on which the quantum fields act as coordinates. We show how to define field-space tensors on this supermanifold from the classical action that are covariant under field reparametrisations. We then employ these tensors to equip the field-space supermanifold with a metric, thus solving a long-standing problem concerning the proper definition of a metric for fermionic theories. With the metric thus defined, we use well-established field-space techniques to extend the VDW effective action and express any fermionic theory in a frame- and field-reparametrisation-invariant manner.